How Do I Find the Point of Inflection in a Cubic Graph?

[garyljc]

Hey guys ,
I'm currently learning curve sketching
and i was thinking ... what would be the best approach towards finding the point of inflection in a cubic graph . Any suggestions ?
Thanks

 

[HallsofIvy]

?? Using the definition- that the second derivative is 0 and the first derivative changes sign there.

 

[garyljc]

What do you mean by changes sign ?
I do understand that the sign change in the first derivative means the gradient
the second derivative means whether the curve is concave or convex ...
that's all i know about the signs so far..
do you mind elaborating more ?
thanks

 

[HallsofIvy]

My mistake, I meant that the second derivative changes sign there: is positive on one side of the inflection point and negative on the other. Yes, second derivative positive means the curve is "convex" upward and second derivative negative means the curve is "convex" downward ("concave" upward). At an inflection point the concavity changes.

 

[garyljc]

i was wondering if there's an definition for convex and concave ... is there ?